# Probabilistic Hysteresis in Integrable and Chaotic Isolated Hamiltonian Systems

## TL;DR

This paper proposes experiments with ultracold atoms to observe how chaos influences irreversibility and hysteresis in isolated Hamiltonian systems, highlighting observable effects of chaotic dynamics on state distributions.

## Contribution

It introduces a feasible experimental setup to study dynamical chaos and hysteresis in quantum systems, linking chaos to irreversibility in a novel way.

## Key findings

- Chaotic dynamics cause observable hysteresis effects.
- Distribution of final states reveals signatures of chaos.
- Irreversibility persists even with slow parameter sweeps.

## Abstract

We propose currently feasible experiments using small, isolated systems of ultracold atoms to investigate the effects of dynamical chaos in the microscopic onset of irreversibility. A control parameter is tuned past a critical value, then back to its initial value; hysteresis appears as a finite probability that the atoms fail to return to their initial state even when the parameter sweep is arbitrarily slow. We show that an episode of chaotic dynamics during part of the sweep time produces distinctive features in the distribution of final states that will be clearly observable in experiments.